The swimmers - Peaty, Francesca Halsall, Jemma Lowe and Chris Walker Hebborn - have already broken their own records, but the ruling means the previous records will now be recognised by the Federation Internationale de Natation, the body that administers international swimming competitions.
The four swimmers had won the 4x100-metre mixed medley at the European championships in Berlin in August 2014 with a time of three minutes and 44 seconds. Peaty also won the 50-metre breaststroke with a time of 26.62 seconds at the same competition. Both times were records in 2014.
But FINA refused to recognise the records because the four had not been tested for the banned substance EPO. Although they had undergone other tests which showed no abnormalities, only a selection of samples at the event were tested for EPO before being destroyed.
FINA rules state that "no world record shall be recognised without a negative doping test certificate for all prohibited substances or prohibited methods identified on the prohibited list for which an analytical technique is available."
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The court of arbitration ruled that the absence of EPO tests "should not fall to the detriment of the athletes and lead to the non-recognition of the world records."
The mixed medley team had already beaten their own record at the world championships in Kazan, Russia, winning the event with a time of three minutes 41.71 seconds. Peaty also broke his 50m breaststroke record in Kazan in the semi-finals with a time of 26.42 seconds.
Neither the 50m breaststroke nor the mixed medley are on the programme for the Rio Olympics in August, but Peaty is also the world 100-metre breaststroke world champion and record holder.
(Reporting by Alan Baldwin, editing by Larry King)
